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A165966 Triangular numbers that are sums of twin prime pairs. 3
36, 120, 276, 300, 2556, 3240, 5460, 8256, 12720, 23436, 26796, 34980, 41616, 46056, 56616, 59340, 103740, 122760, 139656, 147696, 157080, 185136, 195000, 231540, 277140, 333336, 353220, 386760, 401856, 516636, 609960, 860016, 1001820 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are multiples of 12.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A105174(n)*(A105174(n) + 1)/2.

EXAMPLE

36 = 8*9/2 is a term since it is triangular and the sum of the twin primes 17 and 19.

120 = 15*16/2 is a term since it is triangular and the sum of the twin primes 59 and 61.

MATHEMATICA

tri[n_] := n*(n+1)/2; Select[tri /@ Range[10^3], And @@ PrimeQ[#/2 + {-1, 1}] &] (* Amiram Eldar, Dec 27 2019 *)

PROG

(PARI) lista(nn) = {for (n = 1, nn, trg = n*(n+1)/2; if (!(trg % 2) && isprime(trg/2-1) && isprime(trg/2+1), print1(trg, ", ")); ); } \\ Michel Marcus, Oct 16 2013

CROSSREFS

Subsequence of A111163 and of A054735.

Cf. A000217, A001359, A105174.

Sequence in context: A129367 A287861 A242356 * A307939 A254146 A173420

Adjacent sequences:  A165963 A165964 A165965 * A165967 A165968 A165969

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 01 2009

STATUS

approved

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Last modified July 11 23:26 EDT 2020. Contains 335652 sequences. (Running on oeis4.)